A man flies a small airplane from Fargo to Bismarck, North Dakota \( -\cdots \) a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour and 0 minutes. What is the plane's speed in still air, and how fast is the wind blowing? his plane speed equals I the wind speed equals

Let’s break it down in a fun way! The first flight from Fargo to Bismarck, where the trip takes 2 hours against the headwind, gives us the equation: \[ 180 = (p - w) \times 2 \] Here, \( p \) is the plane's speed in still air, and \( w \) is the wind speed. Rearranging gives us \( p - w = 90 \). On the way back, the trip takes only 1 hour with the wind at his back, leading to this equation: \[ 180 = (p + w) \times 1 \] So, \( p + w = 180 \). Now, we can solve these two equations: 1. \( p - w = 90 \) 2. \( p + w = 180 \) Adding those gives \( 2p = 270 \), so \( p = 135 \) mph. To find \( w \), plug \( p \) back into the second equation: \( 135 + w = 180 \), thus \( w = 45 \) mph. So, the plane's speed is 135 mph and the wind speed is 45 mph! To keep your flying adventures safe, remember: always check your weather conditions! Wind speeds can dramatically affect your flight time, as you just learned! Knowing how to calculate your effective speed in varying conditions is crucial for pilots. It can save time, fuel, and lead to safe landing decisions.